# How do you simplify 3 sqrt 12 + 4 sqrt18?

Mar 2, 2018

$6 \sqrt{3} + 12 \sqrt{2}$

#### Explanation:

$3 \sqrt{12} + 4 \sqrt{18}$

$3 \sqrt{4 \cdot 3} + 4 \sqrt{2 \cdot 3 \cdot 3}$

$3 \cdot \sqrt{4} \cdot \sqrt{3} + 4 \cdot \sqrt{2} \cdot \sqrt{3} \cdot \sqrt{3}$

$3 \cdot 2 \cdot \sqrt{3} + 4 \cdot \sqrt{2} \cdot \sqrt{3} \cdot \sqrt{3}$

$6 \cdot \sqrt{3} + 4 \cdot \sqrt{2} \cdot \sqrt{3} \cdot \sqrt{3}$

$6 \cdot \sqrt{3} + 4 \cdot \sqrt{2} \cdot 3$

$6 \sqrt{3} + 12 \sqrt{2}$

(or $6 \left(\sqrt{3} + 2 \sqrt{2}\right)$)

Mar 2, 2018

$6 \sqrt{3} + 12 \sqrt{2}$

#### Explanation:

$3 \sqrt{12} + 4 \sqrt{18}$
$3 \sqrt{4 \cdot 3} + 4 \sqrt{9 \cdot 2}$
$6 \sqrt{3} + 12 \sqrt{2}$
We can't really combine those terms, due to the different numbers under the radicand

Mar 2, 2018

3sqrt12 + 4sqrt18=color(blue)(6sqrt3 + 12sqrt2

#### Explanation:

Simplify:

$3 \sqrt{12} + 4 \sqrt{18}$

Prime factorize $12$ in $\sqrt{12}$.

$3 \sqrt{2 \times 2 \times 3} + 4 \sqrt{18}$

Simplify.

$3 \times 2 \sqrt{3} + 4 \sqrt{18}$

$6 \sqrt{3} + 4 \sqrt{18}$

Prime factorize $18$.

$6 \sqrt{3} + 4 \sqrt{2 \times 3 \times 3}$

Simplify.

$6 \sqrt{3} + 4 \times 3 \sqrt{2}$

$6 \sqrt{3} + 12 \sqrt{2}$